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The short memory principle for solving Abel differential equation of fractional order. (English) Zbl 1236.34008
Summary: The short memory principle (SMP) is applied for solving the Abel differential equation with fractional order. We evaluate the approximate solution at the end of required interval, and construct a suitable iteration scheme employing this end point as initial value. Numerical experiments show that our iteration method is simple and efficient, and that a proper length of memory could maintain the validity of the short memory principle.

MSC:
34A08Fractional differential equations
65L05Initial value problems for ODE (numerical methods)
45J05Integro-ordinary differential equations
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Full Text: DOI
References:
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